Question

(c) suppose the maximum value of 53 was in error and should have been 45. for each statistic, indicate whether this correction would result in an increase, a decrease, or no change. drag each term to the appropriate box. answer bank mean standard deviation median interquartile range increases decreases no change

Explanation:

To solve this, we analyze each statistic when the maximum value (53) is corrected to 45:

1. Mean

The mean is the sum of values divided by the number of values. Since we’re reducing the maximum value (from 53 to 45, a decrease of 8), the total sum decreases. With the number of values unchanged, the mean will decrease.

2. Standard Deviation

Standard deviation measures the spread of data. A smaller maximum value (closer to the mean) reduces the overall spread. Thus, the standard deviation decreases.

3. Median

The median is the middle value (or average of two middle values) when data is ordered. Changing the maximum value (which is at the end of the ordered data) does not affect the middle value(s). So, the median remains unchanged.

4. Interquartile Range (IQR)

IQR is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)), which depend on the middle 50% of data. The maximum value (an extreme value) does not impact \(Q_1\) or \(Q_3\). Thus, IQR remains unchanged.

Final Matching:

• Mean: Decreases
• Standard deviation: Decreases
• Median: No change
• Interquartile range: No change

(To present as drag-and-drop: Drag "Mean" to "Decreases", "Standard deviation" to "Decreases", "Median" to "No change", "Interquartile range" to "No change".)

Answer:

To solve this, we analyze each statistic when the maximum value (53) is corrected to 45:

1. Mean

The mean is the sum of values divided by the number of values. Since we’re reducing the maximum value (from 53 to 45, a decrease of 8), the total sum decreases. With the number of values unchanged, the mean will decrease.

2. Standard Deviation

Standard deviation measures the spread of data. A smaller maximum value (closer to the mean) reduces the overall spread. Thus, the standard deviation decreases.

3. Median

The median is the middle value (or average of two middle values) when data is ordered. Changing the maximum value (which is at the end of the ordered data) does not affect the middle value(s). So, the median remains unchanged.

4. Interquartile Range (IQR)

IQR is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)), which depend on the middle 50% of data. The maximum value (an extreme value) does not impact \(Q_1\) or \(Q_3\). Thus, IQR remains unchanged.

Final Matching:

• Mean: Decreases
• Standard deviation: Decreases
• Median: No change
• Interquartile range: No change

(To present as drag-and-drop: Drag "Mean" to "Decreases", "Standard deviation" to "Decreases", "Median" to "No change", "Interquartile range" to "No change".)